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FromTheMoon [43]
3 years ago
14

Prime factorization of 216 in expanded form

Mathematics
2 answers:
Basile [38]3 years ago
7 0
216|2\\108|2\\.\ 54|2\\.\ 27|3\\.\ \ 9|3\\.\ \ 3|3\\.\ \ 1|\\\\216=2\times2\times2\times3\times3\times3=\huge\boxed{2^3\times3^3}
dem82 [27]3 years ago
5 0
216= 36 \times6 = 6\times 6\times 6  = 6^3 = (2\times 3)^3= \boxed {2^3 \times 3^3}
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The proportion of junior executives leaving large manufacturing companies within three years is to be estimated within 3 percent
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The formulas we use to find the required sample size :-

1. n=(\dfrac{z^*\cdot \sigma}{E})^2

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2. n=p(1-p)(\dfrac{z^*}{E})^2 , where p= prior estimate of population proportion.

3. If prior estimate of population proportion is unavailable , then we take p= 0.5 and the formula becomes

n=0.25(\dfrac{z^*}{E})^2

Given : Margin of error : E= 3% =0.03

Critical value for 95% confidence interval = z*= 1.96

A study conducted several years ago revealed that the percent of junior executives leaving within three years was 21%.

i.e. p=0.21

Then by formula 2., the required sample size will be :

n=0.21(1-0.21)(\dfrac{1.96}{0.03})^2

n=0.21(0.79)(65.3333)^2

n=(0.1659)(4268.44008889)\\\\ n=708.134933333\approx709 [Round to the next integer.]

Hence, the required sample size of junior executives should be studied = 709

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